Method for separating blind signal and apparatus for performing the same

ABSTRACT

A method for separating a blind signal includes: converting mixed signals of a time domain collected by using a plurality of sensors into mixed signals of a frequency domain; calculating a separation filter from the mixed signals which have been converted into those of the frequency domain; calculating an inverse filter of the separation filter; calculating the difference in phase between the respective sensors from the calculated inverse filter; permutation-sorting the separation filter by using the calculated phase difference; and separating the mixed signals of the frequency domain by using the permutation-sorted separation filter.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the priority of Korean Patent Application Nos.10-2009-0127541 filed on Dec. 18, 2009 and 10-2010-0104197 filed on Oct.25, 2010, in the Korean Intellectual Property Office, the disclosures ofwhich are incorporated herein by reference.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a signal processing technique and, moreparticularly, to a blind signal separating method for separatingrespective signals from multi-channel multi-path mixed signals, and anapparatus for performing the same.

2. Description of the Related Art

In general, a plurality of signal sources in a multi-channel multi-pathenvironment reach respective sensors via various paths and are mixed inthe respective sensors. Among the various paths from the locations ofthe signal sources to the sensors, a direct path involves a time delaycorresponding to relative locations of the signal sources and sensors.

An independent component analysis (ICA) technique, using the fact thatsignal sources are statically independent, estimates radio wave paths ofsignal sources from multi-channel signals and separates the signalsources, without any information regarding the signal sources providedin advance.

Also, a frequency domain ICA technique is a method in which an ICA isapplied in each frequency. In this case, because the ICA is separatelyapplied in each frequency, the separated signals are permutated, and oneof the methods for solving such permutation phenomenon is utilizingdirection information of the signals.

The method for separating a blind signal using the frequency domain ICAand the permutation phenomenon will now be described in detail. First,when an nth (n=1, . . . , N) signal source is s_(n)(t) and an impulseresponse from the nth signal source to an mth (m=1, . . . , M) sensor ish_(mn), mixed signals (x_(m)) collected from the mth sensor can berepresented by Equation 1 shown below:

$\begin{matrix}{x_{m} = {\sum\limits_{n}{h_{mn}*s_{n}}}} & \left\lbrack {{Equation}\mspace{14mu} 1} \right\rbrack\end{matrix}$

In Equation 1, * indicates convolution, and the impulse response h_(mn)is a mixture filter administering the process of mixing the signalsources by the convolution. Signal processing is performed in afrequency domain, so mixed signals in a time domain are multiplied by awindow function and then converted into signals of the frequency domainthrough short-time Fourier Transform.

The mixed signals in the frequency domain can be represented by Equation2 shown below:

$\begin{matrix}{{x_{m}\left( {f,t} \right)} = {\sum\limits_{m = 1}^{M}{{H_{mn}(f)}{s\left( {f,t} \right)}}}} & \left\lbrack {{Equation}\mspace{14mu} 2} \right\rbrack\end{matrix}$

In Equation 2, f indicates a frequency index, t indicates a time index,and x_(m)(f,t), H_(mn)(f), s_(n)(f,t) are those obtained as x_(m),h_(m), s_(n) are Fourier-transformed, respectively. In general, theimpulse response h_(mn) changes over time, but hereinafter, it isassumed that the impulse response h_(mn) is time-invariant for the sakeof brevity.

When the signal sources and the mixed signals are defined ass(f,t)=[s₁(f,t),s_(N)(f,t)]^(T) and x(f,t)=[x₁(f,t),x_(n)(f,t)]^(T) in avector form, the mixed signals can be represented by Equation 3 shownbelow:

x(f,t)=H(f)s(f,t)  [Equation 3]

In the frequency domain, ICA with respect to a complex value (CICA:Complex-valued ICA) is separately applied in each frequency to calculatea separation filter W(f). An applicable CICA method includes FastICA (E.Bingham et al., “A fast fixed-point algorithm for independent componentanalysis of complex-valued signals,” International Journal of NeuralSystems, vol. 10, no. 1, pp. 1-8, 2000) or InforMax (M. S. Pederson etal., “A survey of convolutive blind source separation methods,” inMultichannel Speech Processing Handbook, Jacob Benesty and Arden Huang,Eds, Springer, 2007), and the like.

The separated signals with respect to the mixed signals are calculatedas represented by Equation 4 shown below:

y(f,t)=W(f)x(f,t)  [Equation 4]

Because ICA is independently applied to each frequency and thestatistical independence of signals is not related to the order ofsignals and change in amplitude of the signals, the resultantlycalculated separation filters are sorted in random order in eachfrequency and have arbitrary sizes. These ambiguities will be referredto as permutation and scaling ambiguities. Here, the scaling ambiguitycan be solved by a minimum distortion principle.

Also, various methods for solving the permutation problem of thefrequency domain ICA have been proposed, and among the methods, a methodof solving the permutation by using direction information of aseparation filter is advantageous in that it can be employedirrespective of a type of signals and provides excellent performance.

When a far-field model, which disregards a signal echo and considersonly a direct path because the distance between a sensor and a signalsource are sufficiently long, is taken into account, the relationshipbetween the direction of the signal and the mixture filter can berepresented by Equation 5 shown below:

$\begin{matrix}{{H_{mn}(f)} = {\lambda_{mn}{\exp \left( \frac{{j2\pi}\; {fd}_{m}{\sin \left( \theta_{n} \right)}}{v} \right)}}} & \left\lbrack {{Equation}\mspace{14mu} 5} \right\rbrack\end{matrix}$

In Equation 5, λ_(m) indicates an attenuation of a direct path, vindicates a radiowave speed of a signal, and d_(m) and θ_(n) indicatethe position of an mth sensor and a direction angle of an nth signalsource based on the front side of the sensor when the position of areference sensor m′ is set to be 0. The ratio of the direct path can berepresented by Equation 6 shown below:

$\begin{matrix}{{\measuredangle \left( \frac{h_{mn}(f)}{\left. {h_{m^{\prime}n}(f)} \right)} \right)} = {{{2\pi \; {f\left( \frac{d_{m}\sin \; \theta_{n}}{v} \right)}} + {2\pi \; k}} = {{2\pi \; f\; \tau_{mn}} + {2\pi \; k}}}} & \left\lbrack {{Equation}\mspace{14mu} 6} \right\rbrack\end{matrix}$

In Equation 6, τ_(mn) indicates a relative delay time taken for the nthsignal source to reach the mth sensor based on the reference sensor m′.The phase

$\measuredangle \left( \frac{h_{mn}(f)}{\left. {h_{m^{\prime}n}(f)} \right)} \right)$

has a value ranging from −π to π, so when the frequency isf≧1/(2|τ_(mn)|)≧ν/2d_(m), aliasing occurs, and at this time, the integerk has a value not 0.

As for respective streams of the separation filter W(f) obtained fromthe results of ICA, spectral nulls are positioned on a spatial spectrumin the direction of the signal sources in order to remove the remainingsignals other than one signal. In this sense, the separation filter hasinformation regarding the direction of the signal sources, which ismathematically equivalent to a null-beamformer.

Meanwhile, the separation filter is the converse of the mixture filter,so A(f)=W⁻¹(f) obtained by taking the converse of the separation filteris equal to the size of the mixture filter H(f) except for thepermutation. Thus, based on these characteristics, a method ofestimating direction information of a signal source from A(f) andsorting the rows of A(f) such that they have the same directioninformation as the estimated direction information has been proposed.Here, as the scheme of sorting the rows of A(f), the converse of theseparation filter, a k-means clustering scheme is applied. However, whenspatial aliasing occurs due to a wide frequency band of a signal or dueto a large space between sensors, because the k value has a value, not0, a one-to-one corresponding relationship is not maintained between thedirection information and phase information (or time delay information),so the method cannot be employed.

To offset the shortcomings, a method of setting a mixture filter as adirect path model having a time delay and attenuation factor andclustering the rows of A(f) by using the same has been proposed. Ak-means clustering scheme is also applied to this method. However, asthe k-means clustering scheme does not utilize statisticalcharacteristics, its performance may be degraded in an environment inwhich an echo is large or background noise is present. In addition, inorder to accurately normalize a phase, the approximate size of a sensorarray must be known and information regarding the disposition ofsensors, or the like, is required.

Another method for solving the permutation problem is a method ofdirectly using the phase of a separation filter, rather than taking theconverse of the separation filter. However, because this method utilizesW(f) forming a spectrum zero point with respect to a signal source, itcannot be applied to a case in which there are three or more signalsources. Also, this method does not consider statisticalcharacteristics, the performance may be degraded in an area withexcessive echo, and information regarding the size and disposition of asensor array is required.

SUMMARY OF THE INVENTION

An aspect of the present invention provides a method for separating ablind signal capable of solving permutation of a separation filterwithout advance information regarding a sensor array and thus improvingthe separation performance.

Another aspect of the present invention provides an apparatus forseparating a blind signal through the method for separating a blindsignal.

According to an aspect of the present invention, there is provided amethod for separating a blind signal, including: converting mixedsignals of a time domain collected by using a plurality of sensors intomixed signals of a frequency domain; calculating a separation filterfrom the mixed signals which have been converted into those of thefrequency domain; calculating an inverse filter of the separationfilter; calculating the difference in phase between the respectivesensors from the calculated inverse filter; permutation-sorting theseparation filter by using the calculated phase difference; andseparating the mixed signals of the frequency domain by using thepermutation-sorted separation filter.

In the calculating of the difference in phase between the sensors fromthe calculated inverse filter, a certain sensor among the plurality ofsensors may be set as a reference sensor, and the difference between thephase of each row of the matrix of the inverse filter and the phase ofthe row corresponding to the reference sensor may be calculated.

The permutation-sorting of the separation filter may include: estimatinga time delay parameter based on the calculated phase difference;calculating permutation-sorting based on the estimated time delayparameter; and permutation-sorting the separation filter by using thecalculated permutation-sorting.

In the estimating of the time delay parameter, θ which maximizes a costfunction of Equation of

$\begin{matrix}\begin{matrix}{L = {\sum\limits_{f}{\ln \; {p\left( {\Phi (f)} \middle| \theta \right)}}}} \\{= {\sum\limits_{f}{\ln \left\{ {\sum\limits_{l}{\psi_{l}{\prod\limits_{m = 2}^{M}{\prod\limits_{n = 1}^{N}{\sum\limits_{k}{_{\varphi}\left( {m,l,n,k,f} \right)}}}}}} \right\}}}}\end{matrix} & \;\end{matrix}$

(where N_(φ)(m,l,n,k,f)≡N(φ_(mO) _(l) _((n))(f)|τ_(mn),σ_(mn) ²,k),τ_(mn) is a relative delay time for nth signal source to reach mthsensor based on a reference sensor m′, σ_(mn) ² is a variance, k is aconstant, O_(l)(n) is nth element of lth permutation O_(l), φ_(mn)(f) isthe phase difference between an mth row of the matrix of the inversefilter and the reference row m′, ψ_(l)=p(z_(fl)=1), z_(fl) is a latentvariable, and Φ(f) is a phase difference matrix), may be estimated.

In the calculating of the permutation-sorting, a permutation-sortingthat maximizes a posterior probability of a permutation combination ofeach frequency may be calculated by using

$\begin{matrix}{{O_{l}^{*}(f)} = {\underset{l}{\arg \; \max}{p\left( {O_{l}(f)} \middle| {\Phi (f)} \right)}}} \\{= {\underset{l}{\arg \; \max}{{p\left( {{\Phi (f)},{O_{l}(f)}} \right)}.}}}\end{matrix}$

In the permutation-sorting of the separation filter, the whole frequencyband may be divided into a low frequency band and a high frequency bandbased on a predetermined particular frequency, and then thepermutation-sorting may be performed.

According to another aspect of the present invention, there is providedan apparatus for separating a blind signal, including: a sensor unitconfigured to include a plurality of sensors each collecting a mixedsignal; a DFT unit converting mixed signals of a time domain providedfrom the sensors into mixed signals of a frequency domain; anindependent component analyzing unit calculating a separation filterfrom the mixed signals which have been converted into those of thefrequency domain; a permutation-sorting unit calculating an inversefilter of the separation filter, calculating a phase difference betweensensors from the calculated inverse filter, and permutation-sorting theseparation filter by using the calculated phase difference; and a signalseparating unit separating the mixed signals of the frequency domain byusing the permutation-sorted separation filter.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and other aspects, features and other advantages of thepresent invention will be more clearly understood from the followingdetailed description taken in conjunction with the accompanyingdrawings, in which:

FIG. 1 is a flow chart illustrating the process of a method forseparating a blind signal according to an exemplary embodiment of thepresent invention;

FIG. 2 is flow chart illustrating a process of estimating a parameterillustrated in FIG. 1;

FIG. 3 is a schematic block diagram of an apparatus for separating ablind signal according to an exemplary embodiment of the presentinvention;

FIGS. 4 a, 4 b and 4 c are view illustrating an environment forevaluating the method for separating a blind signal according to anexemplary embodiment of the present invention;

FIG. 5 is graphs showing the results of evaluation of performance of themethod for separating a blind signal according to an exemplaryembodiment of the present invention; and

FIG. 6 is a table showing the results of evaluation of performance ofthe method for separating a blind signal according to an exemplaryembodiment of the present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

The present invention will now be described more fully hereinafter withreference to the accompanying drawings, in which preferred embodimentsof the invention are shown.

However, it should be understood that the following exemplifyingdescription of the invention is not meant to restrict the invention tospecific forms of the present invention but rather the present inventionis meant to cover all modifications, similarities and alternatives whichare included in the spirit and scope of the present invention. The termsused in the present application are merely used to describe particularembodiments, and are not intended to limit the present invention. Unlessotherwise defined, all terms used herein, including technical orscientific terms, have the same meanings as those generally understoodby those with ordinary knowledge in the field of art to which thepresent invention belongs. Such terms as those defined in a generallyused dictionary are to be interpreted to have the meanings equal to thecontextual meanings in the relevant field of art, and are not to beinterpreted to have ideal or excessively formal meanings unless clearlydefined in the present application.

Embodiments of the present invention will be described below in detailwith reference to the accompanying drawings, where those components arerendered the same reference number that are the same or are incorrespondence, regardless of the figure number, and redundantexplanations are omitted.

FIG. 1 is a flow chart illustrating the process of a method forseparating a blind signal according to an exemplary embodiment of thepresent invention. The method is performed by an apparatus forseparating a blind signal. FIG. 2 is flow chart illustrating a processof estimating a parameter illustrated in FIG. 1.

With reference to FIGS. 1 and 2, first, the blind signal separatingapparatus collects N (N is a natural number) number of signal sources,which have reached through multiple paths, through M (M is a naturalnumber) number of sensors and stores the mixed signals x_(m)(m=1, M)collected through the M number of sensors (step 101).

Next, the blind signal separating apparatus converts the collected mixedsignals x_(m) of a time domain into signals x_(m)(f,t) of a frequencydomain through short-time Fourier transform (step 103). Here, the mixedsignals x_(m) of the time domain are multiplied by a window function andthen converted into the signals of the frequency domain. As the windowfunction, a hamming window may be used. Here, f indicates a frequencyindex, and t indicates a time index.

The blind signal separating apparatus independently and separatelyprocesses the mixed signals x_(m)(f,t), which have been converted intothose of the frequency domain, in each frequency f by using anindependent component analysis (ICA) to calculate a separation filtermatrix W(f) (step 105). Here, the separation filter matrix W(f) is in arandomly permuted state, so a permutation-sorting process is required.

For the permutation-sorting, first, the blind signal separatingapparatus calculates an inverse matrix (or an inverse filter)A(f)=W⁻¹(f) of the separation filter matrix W(f) (step 107).

Thereafter, the blind signal separating apparatus performspermutation-sorting by using direction information of the inverse matrixA(f) of the separation filter.

To this end, first, the blind signal separating apparatus calculates aphase difference matrix Φ(f) from the inverse matrix (or an inversefilter matrix) A(f) of the separation filter (step 109). Here, the blindsignal separating apparatus may use a Gaussian mixture model withrespect to the phase difference.

In detail, the blind signal separating apparatus calculates thedifference in phase between mth row of the inverse filter A(f) of theseparation filter and a reference row m′ as represented by Equation 7shown below:

$\begin{matrix}{{{\varphi_{mn}(f)} = {\measuredangle \left( \frac{a_{mn}(f)}{\left. {a_{m^{\prime}n}(f)} \right)} \right)}},\begin{matrix}{{m = 1},\ldots \mspace{14mu},M,{m \neq m^{\prime}}} \\{{n = 1},\ldots \mspace{14mu},N}\end{matrix}} & \left\lbrack {{Equation}\mspace{14mu} 7} \right\rbrack\end{matrix}$

When there is an echo and noise, the average of the phase differenceφ_(mn)(f) may be represented as a random variable of Gaussianprobability distribution having an average phase difference of 2πτ_(mn)and a variance of σ_(mn) ².

$\begin{matrix}{{p\left( {\left. {\varphi_{mn}(f)} \middle| \tau_{mn} \right.,\sigma_{mn}^{2},k} \right)} = {{\left( {\left. {\varphi_{mn}(f)} \middle| \tau_{mn} \right.,\sigma_{mn}^{2},k} \right)} = {\frac{1}{\sqrt{2\pi \; \sigma_{mn}^{2}}}{\exp\left( {- \frac{\left( {{\varphi_{mn}(f)} + {2\pi \; k} - {2\pi \; f\; \tau_{mn}}} \right)^{2}}{2\sigma_{mn}^{2}}} \right)}}}} & \left\lbrack {{Equation}\mspace{14mu} 8} \right\rbrack\end{matrix}$

In Equation 8, a constant k has an integer value, not 0, when there isaliasing. The integer value is determined by (f,τ_(mn)) and may be setwithin a limited range from −K to K. Here, K may be determined to bedifferent in each frequency according to the disposition and size of thesensor array. When the size of the sensor array is not accurately known,a sufficient larger value may be set.

The probability distribution of φ_(mn)(f) with respect to everyavailable k value can be represented by Equation 9 shown below:

$\begin{matrix}{{p\left( {\left. {\varphi_{mn}(f)} \middle| \tau_{mn} \right.,\sigma_{mn}^{2}} \right)} = {{\sum\limits_{k = {- K}}^{K}{\left( {\left. {\varphi_{mn}(f)} \middle| \tau_{mn} \right.,\sigma_{mn}^{2},k} \right)}} = {\sum\limits_{k = {- K}}^{K}{\frac{1}{\sqrt{2\pi \; \sigma_{mn}^{2}}}{\exp\left( {- \frac{\left( {{\varphi_{mn}(f)} + {2\pi \; k} - {2\pi \; f\; \tau_{mn}}} \right)^{2}}{2\sigma_{mn}^{2}}} \right)}}}}} & \left\lbrack {{Equation}\mspace{14mu} 9} \right\rbrack\end{matrix}$

In order to solve the permutation problem, a combination of permutationsthat can be generated is defined as O={O₁, . . . , O_(l), . . . ,O_(P)}. Here, P=N! Also, in order to solve the permutation problem byusing an expectation maximization scheme, a latent variable z_(fl) isdefined as follows.

(1) When the inverse matrix A(f) of the separation filter corresponds topermutation 01 in the frequency f, z_(fl) has a value of 1.

(2) When

${\psi_{l} = {p\left( {z_{fl} = 1} \right)}},{{\sum\limits_{l}\psi_{l}} = 1.}$

When a reference sensor is set to be m′=1 for simplifying the formula,the phase difference may be expressed as a matrix as represented byEquation 10 shown below;

$\begin{matrix}{{\Phi (f)} = \begin{bmatrix}{\varphi_{21}(f)} & \ldots & {\varphi_{2N}(f)} \\\vdots & \ddots & \vdots \\{\varphi_{M\; 1}(f)} & \ldots & {\varphi_{MN}(f)}\end{bmatrix}} & \left\lbrack {{Equation}\mspace{14mu} 10} \right\rbrack\end{matrix}$

When it is assumed that the respective phase differences arestatistically independent from each other, a probability distributionwhen it is assumed that an observed phase difference corresponds to apermutation 0₁ can be expressed as represented by Equation 11 shownbelow:

$\begin{matrix}{{p\left( {\left. {\Phi (f)} \middle| z_{fl} \right. = 1} \right)} = {\prod\limits_{m = 2}^{M}{\prod\limits_{n = 1}^{N}{\sum\limits_{k = {- K}}^{K}{\left( {\left. {\varphi_{m\; {O_{l}{(n)}}}(f)} \middle| \tau_{mn} \right.,\sigma_{mn}^{2},k} \right)}}}}} & \left\lbrack {{Equation}\mspace{14mu} 11} \right\rbrack\end{matrix}$

In Equation 11, 0₁(n) is nth element of a first permutation 0₁. Also,the sum of m is for considering the phase difference of all the sensorswith respect to the reference sensor.

From the foregoing model, the probability of Φ(f) can be represented byEquation 12 by averaging all the permutations.

$\begin{matrix}{{p\left( {\Phi (f)} \middle| \theta \right)} = {\sum\limits_{l = 1}^{P}{\psi_{l}{p\left( {{\left. {\Phi (f)} \middle| z_{fl} \right. = 1},\theta} \right)}}}} & \left\lbrack {{Equation}\mspace{14mu} 12} \right\rbrack\end{matrix}$

Also, the blind signal separating apparatus estimates a time delayparameter in order to solve the permutation from the calculated phasedifference as described above (step 111).

The process of estimating a parameter will now be described in detailwith reference to FIG. 2. First, the blind signal separating apparatusdivides the whole frequency band into a low frequency band and a highfrequency band (step 111-1).

Next, the blind signal separating apparatus defines a parameter to beestimated for the low frequency band as θ={τ_(mn),σ_(mn) ²,ψ_(l)}, andinitializes the parameter θ={τ_(mn),σ_(mn) ²,ψ_(l)} with respect to thelow frequency band with a suitable value (step 111-3). Here, it isdefined as N_(φ)(m,l,n,k,f)≡N(φ_(mO) _(l) _((n))(f)|τ_(mn),σ_(mn) ²,k)in order to simplify the formula representation.

In estimating the parameter θ, in a state in which a previous parameterθ^(old) is given, θ, which maximizes a cost function as represented inEquation 13, is estimated by using an expectation-maximization (EM)technique.

$\begin{matrix}\begin{matrix}{L = {\sum\limits_{f}{\ln \; {p\left( {\Phi (f)} \middle| \theta \right)}}}} \\{= {\sum\limits_{f}{\ln \left\{ {\sum\limits_{l}{\psi_{l}{\prod\limits_{m = 2}^{M}{\prod\limits_{n = 1}^{N}{\sum\limits_{k}{_{\varphi}\left( {m,l,n,k,f} \right)}}}}}} \right\}}}}\end{matrix} & \left\lbrack {{Equation}\mspace{14mu} 13} \right\rbrack\end{matrix}$

To this end, first, when the parameter is given, the blind signalseparating apparatus calculates posterior probability β_(fl) of thepermutation in the frequency f as represented by Equation 14 shown below(step 111-5).

$\begin{matrix}\begin{matrix}{\beta_{fl} = {p\left( {{z_{fl} = \left. 1 \middle| {\Phi (f)} \right.},\theta^{old}} \right)}} \\{= \frac{\psi_{l}{\prod\limits_{n}{\prod\limits_{m}{\sum\limits_{k}{_{\varphi}\left( {m,l,n,k,f} \right)}}}}}{\sum\limits_{l}{\psi_{l}{\prod\limits_{n}{\prod\limits_{m}{\sum\limits_{k}{_{\varphi}\left( {m,l,n,k,f} \right)}}}}}}}\end{matrix} & \left\lbrack {{Equation}\mspace{14mu} 14} \right\rbrack\end{matrix}$

And then, an auxiliary function is defined as follows.

$\begin{matrix}{{Q\left( \theta \middle| \theta^{old} \right)} = {\sum\limits_{f}{\sum\limits_{l}{\beta_{fl}\ln \left\{ {\phi_{l}{\prod\limits_{m = 2}^{M}{\prod\limits_{n = 1}^{N}{\sum\limits_{k}{_{\varphi}\left( {m,l,n,k,f} \right)}}}}} \right\}}}}} & \left\lbrack {{Equation}\mspace{14mu} 15} \right\rbrack\end{matrix}$

Thereafter, the parameter θ, which maximizes Equation 15, is calculatedas represented by Equation 16 to Equation 18 shown below (step 111-7).

$\begin{matrix}{\left( \tau_{m^{*}n^{*}} \right)^{new} = \frac{\sum\limits_{fl}{\beta_{fl}\gamma_{fl}^{\prime}}}{\sum\limits_{fl}{\beta_{fl}2\pi \; f^{2}}}} & \left\lbrack {{Equation}\mspace{14mu} 16} \right\rbrack \\{\left( \sigma_{m^{*}n^{*}}^{2} \right)^{new} = \frac{\sum\limits_{fl}{\beta_{fl}\gamma_{fl}^{''}}}{\sum\limits_{fl}\beta_{fl}}} & \left\lbrack {{Equation}\mspace{14mu} 17} \right\rbrack \\{\left( \psi_{l} \right)^{new} = {\frac{1}{F}{\sum\limits_{f}\beta_{fl}}}} & \left\lbrack {{Equation}\mspace{14mu} 18} \right\rbrack\end{matrix}$

The estimated value with respect to ψ_(l) expressed in Equation 18 canbe calculated by optimizing Equation 1 such that it satisfies thecondition of

${\sum\limits_{l}\psi_{l}} = 1.$

Also, in Equation 18, F indicates the total number of discretefrequencies.

In Equation 16, y′_(fl) is expressed as shown in Equation 19 below, andin Equation 17, γ″_(fl) is expressed as shown in Equation 20 below:

$\begin{matrix}{\mspace{20mu} {\gamma_{fl}^{\prime} = \frac{\sum\limits_{k}{{_{\varphi}\left( {m^{*},l,n^{*},k,f} \right)}\left( {{\varphi_{m^{*}{O_{l}{(n^{*})}}}(f)} + {2\pi \; k}} \right)f}}{\sum\limits_{k}{_{\varphi}\left( {m^{*},l,n^{*},k,f} \right)}}}} & \left\lbrack {{Equation}\mspace{14mu} 19} \right\rbrack \\{\mspace{20mu} {\gamma_{fl}^{''} = \frac{\sum\limits_{k}{{_{\varphi}\left( {m^{*},l,n^{*},k,f} \right)}\begin{pmatrix}{{\varphi_{m^{*}{O_{l}{(n^{*})}}}(f)} +} \\{{2\pi \; k} - {2\pi \; f\; \tau_{m^{*}n^{*}}}}\end{pmatrix}^{2}}}{\sum\limits_{k}{_{\varphi}\left( {m^{*},l,n^{*},k,f} \right)}}}} & \left\lbrack {{Equation}\mspace{14mu} 20} \right\rbrack\end{matrix}$

Thereafter, the blind signal separating apparatus calculates alikelihood ratio function Q(θ|θ^(old)) by using Equation 15 (step111-9).

Then, the blind signal separating apparatus determines whether or notthe parameter estimation has been converged based on the previouslylikelihood ratio function calculation results (step 111-11). When it isdetermined that the parameter estimation has not been converged, theblind signal separating apparatus returns to step 111-3 and repeatedlyperforms steps 111-3 to 111-11.

When it is determined that the parameter estimation has beensufficiently converged in step 111-11, the blind signal separatingapparatus performs step 111-13 to initialize the parameterθ={τ_(mn),σ_(mn) ²,ψ_(l)} with respect to the high frequency band with aproper value (step 111-13).

Thereafter, the blind signal separating apparatus performs steps 111-15to 111-21 in the same manner as steps 111-5 to 111-11 preformed at thelow frequency band, to estimate a parameter with respect to the highfrequency band.

When the estimation of the parameter is completed according to theprocess illustrated in FIG. 2, the blind signal separating apparatuscalculates permutation-sorting O_(l)(f) (step 113). To this end, first,the blind signal separating apparatus calculates a joint probabilitybetween an observed phase difference and a permutation as represented byEquation 21 shown below:

$\begin{matrix}{{p\left( {{\Phi (f)},{O_{l}(f)}} \right)} = {\psi_{l}{\prod\limits_{m}{\prod\limits_{n}{\sum\limits_{k}{_{\varphi}\left( {m,l,n,k,f} \right)}}}}}} & \left\lbrack {{Equation}\mspace{14mu} 21} \right\rbrack\end{matrix}$

A posterior probability of the phase difference over the permutationgiven by the Bayes rule can be represented by Equation 22 shown below:

$\begin{matrix}\begin{matrix}{{p\left( {O_{l}(f)} \middle| {\Phi (f)} \right)} = \frac{p\left( {{\Phi (f)},{O_{l}(f)}} \right)}{p\left( {\Phi (f)} \right)}} \\{= \frac{p\left( {{\Phi (f)},{O_{l}(f)}} \right)}{\sum\limits_{l}{p\left( {{\Phi (f)},{O_{l}(f)}} \right)}}}\end{matrix} & \left\lbrack {{Equation}\mspace{14mu} 22} \right\rbrack\end{matrix}$

A desired permutation-sorting can be determined as represented byEquation 23 shown below, from Equation 22, such that the posteriorprobability is maximized.

$\begin{matrix}\begin{matrix}{{O_{l}^{*}(f)} = {\underset{l}{\arg \; \max}{p\left( {O_{l}(f)} \middle| {\Phi (f)} \right)}}} \\{= {\underset{l}{\arg \; \max}{p\left( {{\Phi (f)},{O_{l}(f)}} \right)}}}\end{matrix} & \left\lbrack {{Equation}\mspace{14mu} 23} \right\rbrack\end{matrix}$

Thereafter, the blind signal separating apparatus performspermutation-sorting on the separation filter W(f0 by using thepermutation-sorting of Equation 23 (step 115), and then separates themixed signals by using the separation filter of whichpermutation-sorting has been solved (step 117).

And then, the blind signal separating apparatus outputs and stores theseparated signals (step 119).

FIG. 3 is a schematic block diagram of an apparatus for separating ablind signal according to an exemplary embodiment of the presentinvention.

With reference to FIG. 3, the blind signal separating apparatusaccording to an exemplary embodiment of the present invention mayinclude a sensor unit 310, a DFT unit 320, an independent componentanalyzing unit 330, a permutation-sorting unit 340, a signal separatingunit 350, an IFFT (Inverse Fast Fourier Transform) unit 360, and astorage unit 370.

The sensor unit 310 may include a plurality of microphones (sensors)configured in the form of an array, and each of the sensors collectsmixed signals x_(m)(m=1, M) of multiple paths. Here, the mixed signalsx_(m) collected through the sensor unit 310 may be provided to the DFTunit 320 and, simultaneously, stored in the storage unit 370.

The DFT unit 320 receives the mixed signals x_(m) of the time domainfrom the sensor unit 310 and performs discrete Fourier transform on thereceived mixed signals x_(m) to convert them into signals x_(m)(f,t) ofthe frequency domain. Here, the DFT unit 320 may multiply the collectedmixed signals x_(m) of the time domain by a window function and thenconvert them into the signals x_(m)(f,t) of the frequency domain throughthe short-time Fourier transform.

The independent component analyzing unit 330 receives the mixed signalsx_(m)(f,t) which have been converted into those of the frequency domain,from the DFT unit 320 and performs independent component analysis (ICA)on the received signals to calculate a separation filter matrix W(f)with respect to each frequency f.

The permutation-sorting unit 340 calculates an inverse matrix A(f) ofthe separation filter matrix W(f) provided from the independentcomponent analyzing unit 330, calculates a phase difference matrix fromthe inverse matrix A(f), calculates permutation-sorting by estimating atime delay parameter from the phase difference, and then sorts thepermutation of the separation filter matrix W(f).

Here, the permutation-sorting unit 340 may perform the steps 107 to 115in FIGS. 1 and 2, so a detailed description thereof will be omitted.

The signal separating unit 350 separates the mixed signals by using theseparation filter, whose permutation has been sorted, provided from thepermutation-sorting unit 340.

The IFFT unit 360 performs IFFT on the separated signals of thefrequency domain provided from the signal separating unit 350 to convertthem into signals of the time domain.

The storage unit 370 stores the signals which have been converted intothose of the time domain.

The DFT unit 320, the independent component analyzing unit 330, thepermutation-sorting unit 340, the signal separating unit 350, and theIFFT (Inverse Fast Fourier Transform) unit 360 may be implemented in theform of a software program which can be read from an informationprocessing device such as a computer, or the like, and executed, or maybe implemented in the form of hardware, such as specifically devisedASIC (Application Specific Integrated Circuits), a digital signalprocessor, or the like, or a combination of hardware and software.

For example, when the blind signal separating apparatus as illustratedin FIG. 3 is implemented as a software program and executed in acomputer, in a conference room in which people are present, the voicesof people or music and background noise are collected through amicrophone array (namely, the sensor unit 310) and transmitted to thecomputer. The computer performs the signal separation process asillustrated in FIGS. 1 and 2 to separate the mixed signals intoindependent signals. Through this process, the background noise, whichwas included in the mixed signals, is canceled, and the noise-canceledsignals are recorded or stored. The stored separation signals may betransmitted to a voice recognizing device (or a voice/audiocommunication device). Here, when the voice recognizing device is inuse, the separated voice is interpreted by the voice recognizing deviceso as to be converted into a computer command or characters, and when avoice coding device is in use, a call having clearer sound quality canbe provided. In this manner, the blind signal separating apparatus canbe utilized as a pre-processor of a voice recognizing device or a voicecommunication device.

FIGS. 4 a, 4 b and 4 c are view illustrating an environment forevaluating the method for separating a blind signal according to anexemplary embodiment of the present invention.

As shown in FIG. 4 a, the sensor (microphone) and a signal source (voicesignal) were disposed to evaluate the performance of the blind signalseparating method. The signal used for the performance, evaluationexperiment was a voice signal sampled by 16 kHz and had a length of 10seconds.

Mixed signals were acquired by measuring an impulse response in anactual laboratory space as shown in FIGS. 4 a, 4 b and 4 c and thenconvoluting it with a voice signal by using a computer. In this case, anecho time of the experiment space was measured to be approximately 500msec.

The mixed signals collected by the sensor (microphone) were selectedwith a hamming window having a length of 2048 samples so as to have a50% overlap and then converted into signals of the frequency domainthrough FFT (Fast Fourier Transform).

In the performance evaluation experiment, the performances of variouscombinations of microphone-voice signals were compared. A separationperformance was expressed by a SIR (Signal-to-Interference Ratio), andan SDR (Signal-to-Distortion Ratio). Here, the separation performancewas calculated by using BSS EVAL MATLAB Toolbox (R. Gribonval, C.Fevotte, and E. Vincent, BSS EVAL Toolbox User GuideRevision 2.0, IRISATechnical Report 1706, April 2005).

In the performance evaluation experiment, the low frequency and highfrequency bands were classified based on 1562.5 Hz (discrete frequencyindex f=200).

In order to use a proper initial value required for a sufficientconvergence in a parameter estimation process, τ_(mn) was initialized asshown in FIG. 4 c. Also, other parameters were initialized into σ_(mn)²1 and ψ_(l)=1/P, respectively. The initial values were uniformlyapplied to every m. It was noted that, even without informationregarding the size and disposition of the sensor array, the initialvalues were sufficiently converged with respect to various combinationsof sensors and signal sources including the combination shown in FIG. 4b.

FIG. 5 is graphs showing the results of evaluation of performance of themethod for separating a blind signal according to an exemplaryembodiment of the present invention, and FIG. 6 is a table showing theresults of evaluation of performance of the method for separating ablind signal according to an exemplary embodiment of the presentinvention.

FIGS. 5 a, 5 b, and 5 c show the phase difference results before andafter the permutation-sorting performed on the m=2nd, 3rd, and 4th rowswhen the first row (m′=1) of A(f) was set as a reference sensor, in thecase of four signal sources (six ones in case of FIG. 4 b). The resultsshow the basic characteristics of the permutation-sorting usingdirection information of the signal sources.

The results illustrated in FIG. 5 reveal the fact that as the intervalbetween sensors is short, a time delay is relatively small, so thepermutation-sorting in the low frequency band is not easy, while thepermutation-sorting is relatively easy in the high frequency band.Meanwhile, when the interval between sensors is large, sorting of thefrequency band is easy, but in the high frequency band, phase differencepatterns becomes complicated due to aliasing, making sorting atintersection points difficult. This problem can be improved by using allthe pairs of sensors (every m), rather than using only a pair of sensors(one m) in Equation 10 and Equation 11. This phenomenon can be confirmedthrough the performance evaluation results illustrated in FIG. 6. InFIG. 6, EM-1 shows the case in which only one pair of sensors is used,and EM-A11 shows the case in which all the pairs of sensors are used.

FIG. 6 shows the results obtained by comparing the blind signalseparating method according to an exemplary embodiment of the presentinvention from the related method (H. Sawada et al. “Solving thepermutation problem of frequency-domain BSS when spatial aliasing occurswith wide sensor spacing, in Proc. ICASSP 2006).

The conventional Sawada method does not use statistical characteristics,so an initial estimated value at the low frequency band is not precise,or when the phase patterns of the high frequency band are complicated,clustering in the vicinity of the intersection points of the phasepatterns fails. This kind of error tends to be reflected in the finalresults as it is, without being corrected. This problem may be reducedto a degree by setting the reference sensor as a central sensor of thesensor array, but in this case, information regarding the disposition ofthe sensor array is required.

In comparison, the blind signal separating method according to anexemplary embodiment of the present invention provides substantially thesame separation performance without the necessity of the size anddisposition of the sensor array. Also, when the information regardingthe sensor array such as the disposition of the sensors, or the like,the time delay can be converted into the direction of signal sources inEquation 6 and Equation 7. Thus, the direction of the signal sources canbe estimated through the blind signal separating method according to anexemplary embodiment of the present invention.

As described above, in the blind signal separating method according toan exemplary embodiment of the present invention, because everyinformation regarding the mixed signals collected from all the sensorsare effectively used, the performance of signal separation can beimproved, the selection of the reference sensor does not substantiallyaffect the separation performance, and the constantly uniform signalseparation performance can be obtained without advance informationregarding the disposition of the sensors and signal sources. Inaddition, when the information regarding the disposition of the sensorsis acquired, the direction of the signal sources can be accuratelycalculated.

As set forth above, according to exemplary embodiments of the invention,because permutation problem of a separation filter is solved by usingthe statistical characteristics, an excellent separation performance canbe provided even in an environment in which there is excessive echo,without advance information regarding the size of a sensor array or thedisposition of sensors. Also, a time delay calculated by using themethod according to an exemplary embodiment of the present invention canbe utilized for estimating the direction of a signal source by using theinformation regarding the sensor disposition.

While the present invention has been shown and described in connectionwith the exemplary embodiments, it will be apparent to those skilled inthe art that modifications and variations can be made without departingfrom the spirit and scope of the invention as defined by the appendedclaims.

1. A method for separating a blind signal, the method comprising:converting mixed signals of a time domain collected by using a pluralityof sensors into mixed signals of a frequency domain; calculating aseparation filter from the mixed signals which have been converted intosignals of the frequency domain; calculating an inverse filter of theseparation filter; calculating the difference in phase between therespective sensors from the calculated inverse filter;permutation-sorting the separation filter by using the calculated phasedifference; and separating the mixed signals of the frequency domain byusing the permutation-sorted separation filter.
 2. The method of claim1, wherein, in the calculating of the difference in phase between thesensors from the calculated inverse filter, a certain sensor, among theplurality of sensors, is set as a reference sensor, and the differencebetween the phase of each row of the matrix of the inverse filter andthe phase of the row corresponding to the reference sensor iscalculated.
 3. The method of claim 1, wherein the permutation-sorting ofthe separation filter comprises: estimating a time delay parameter basedon the calculated phase difference; calculating permutation-sortingbased on the estimated time delay parameter; and permutation-sorting theseparation filter by using the calculated permutation-sorting.
 4. Themethod of claim 3, wherein in the estimating of the time delayparameter, θ which maximizes a cost function of Equation of$\begin{matrix}\begin{matrix}{L = {\sum\limits_{f}{\ln \; {p\left( {\Phi (f)} \middle| \theta \right)}}}} \\{= {\sum\limits_{f}{\ln \left\{ {\sum\limits_{l}{\psi_{l}{\prod\limits_{m = 2}^{M}{\prod\limits_{n = 1}^{N}{\sum\limits_{k}{_{\varphi}\left( {m,l,n,k,f} \right)}}}}}} \right\}}}}\end{matrix} & \;\end{matrix}$ (where N_(φ)(m,l,n,k,f)≡N(φ_(mO) _(l)_((n))(f)|τ_(mn),σ_(mn) ²,k), τ_(mn) is a relative delay time for nthsignal source to reach mth sensor based on a reference sensor m′, σ_(mn)² is a variance, k is a constant, O_(l)(n) is nth element of lthpermutation O_(l), φ_(mn)(f) is the phase difference between an mth rowof the matrix of the inverse filter and the reference row m′,ψ_(l)=p(z_(fl)=1), z_(fl) is a latent variable, and Φ(f) is a phasedifference matrix) is estimated.
 5. The method of claim 4, wherein, inthe calculating of the permutation-sorting, a permutation-sorting thatmaximizes a posterior probability of a permutation combination of eachfrequency is calculated by using $\begin{matrix}{{O_{l}^{*}(f)} = {\underset{l}{\arg \; \max}{p\left( {O_{l}(f)} \middle| {\Phi (f)} \right)}}} \\{= {\underset{l}{\arg \; \max}{{p\left( {{\Phi (f)},{O_{l}(f)}} \right)}.}}}\end{matrix}$
 6. The method of claim 1, wherein, in thepermutation-sorting the separation filter, the whole frequency band isdivided into a low frequency band and a high frequency band based on apredetermined particular frequency, and then the permutation-sorting isperformed.
 7. An apparatus for separating a blind signal, the apparatuscomprising: a sensor unit configured to include a plurality of sensorseach collecting a mixed signal; a DFT unit converting mixed signals of atime domain provided from the sensors into mixed signals of a frequencydomain; an independent component analyzing unit calculating a separationfilter from the mixed signals which have been converted into those ofthe frequency domain; a permutation-sorting unit calculating an inversefilter of the separation filter, calculating a phase difference betweensensors from the calculated inverse filter, and permutation-sorting theseparation filter by using the calculated phase difference; and a signalseparating unit separating the mixed signals of the frequency domain byusing the permutation-sorted separation filter.
 8. The apparatus ofclaim 7, wherein the permutation-sorting unit sets a certain sensor,among the plurality of sensors, as a reference sensor, and calculatesthe difference in phase between the phase of each row of the matrix ofthe inverse filter and the phase of the row corresponding to thereference sensor.
 9. The apparatus of claim 7, wherein thepermutation-sorting unit estimates a time delay parameter based on thecalculated phase difference, calculates a permutation-sorting based onthe estimated time delay parameter, and permutation-sorts the separationfilter by using the calculated permutation-sorting.
 10. The apparatus ofclaim 7, wherein the permutation-sorting unit performspermutation-sorting by dividing the whole frequency band into a lowfrequency band and a high frequency band based on a predeterminedparticular frequency.